In several ways, the three previous posts on Representation have just been a warm up. The table was set beautifully to frame the spicy entree of Pictures, an obligatory fishy dish of Diagrams and a long and luxurious main course of Stories. Now it’s the lip quivering anticipation of a pudding of sweet Metaphor.

That wasn’t a Metaphor. Metaphors – from the Greek to transfer – shift meaning sideways from one thing to a completely different thing. The purpose is mostly to expand the perception of what things are like and importantly, how they may behave. The above paragraph is mostly an analogy – which means proportion – to compare the qualities of two things with a common logical route. In other words, to explain a series of interrelated posts by using a dinner menu that is logically similar but simpler and more familiar to the person getting the explanation. I hope that makes sense, this next bit might not.

Representation – The Big Middle One, explained Stories as a form of Representation that sets a thing into its context in real space and time. Whereas Diagrams could be used to simplify a Story to explain things, a Metaphor extends the Story by abstracting it to a sense of what could be learnt from it. Although Metaphors, similarly to Diagrams, reduce the volume inherent in a Story, Metaphors are designed to expand its meaning, providing a frame through which people can consider a thing’s function: what the thing is for.

Metaphors are Models. At least in Representative terms, a thing that can be called a Model transfers meaning from something uncertain to understand, visualise and even predict, how that thing may behave under different conditions. Therefore Metaphors work best to represent things, when the thing is placed within some future situation or set of constraints, to imagine what could happen.

Subsequently, a popular and legitimate use of Models is to help people consider what might happen in the future given a certain scenario, to simulate those situations or conditions, ahead of actually experiencing them. Health warning, people are shit at predicting how they will behave in the future, which is why highly immersed simulation for people who work under pressure, is not called training, it’s called preparation.

To expand upon my previous allusion to fashion models: they are in fact an excellent albeit quite manipulative, example of a Metaphor, as they provide people with an imaginary model of the future. The glamour, the perfection, the arrogant superiority, the sheer style and a hundred other things that fill the minds of the people alongside the catwalks imagining how amazing they’ll look and feel in that coat. Almost nobody in the crowd has the body or performance attitude of the Supermodel, but that doesn’t matter. Models and Metaphors can be extremely persuasive, which is why they are firmly routed in both our anthropological history and contemporary cognitive sciences. Models are also ubiquitous amongst management gurus and other unscrupulous pedlars.

With that in mind I’d better own up to using a couple of little Metaphors in the previous posts, mainly as the prompts for you to imagine things: existential bricks, mechanical tea spoons and emotional time travelling. Imagination is simultaneously our most powerful gift and most manipulable curse.

The other principle use of Metaphor is to try to understand something at the edge of your comprehension, something just out of reach. If you can reach a thing, it’s physical presence, then you can watch what it does, test it, take it apart, break it or try to make another one. But if a thing or a concept is just out of reach so that you cannot sufficiently interact with it, then a Metaphor is a tool to help you imagine what, where, when, how and mostly the why of something.

Metaphors (and Models) are not new. Before mathematics and equations were invented, the great thinkers, educators and scientists used Metaphors to explain the universe. Their lessons were often embedded in grand stories of trial and tribulation and righteous gods and devious monsters, doing things like ordinary people do: procreating, fighting, coveting, fighting and so on. In ancient times – not so ancient for some cultures – when people asked their wise old souls to explain how the universe worked, they used stories about these Gods laying waste to each other, forming islands with their bodies and bringing things into creation through pure will. This is a clever way of engaging an otherwise uneducated society, in thinking about the world – less times tables more cryptic crossword. Their lessons, in strings of lovely Metaphor, have endured a very long time, for example the famous Metaphor, that the world rides through the heavens on the back of a giant turtle.

Now to our modern cultured minds, that may seem like a story you tell children, just like a beardy old bloke who lives on a cloud. So imagine the people on some tropical island who live with the turtles, they see turtles all the time and know a bit about turtles. Turtles emerge from the sand and disappear into the sea, they return home years later and some older familiar turtles are seen swimming free in the shallows near the beach. So they are free to swim and we don’t know where to, or why, but they return with some regularity, so there is clearly some higher purpose. Now imagine those people trying to understand their own place in the universe. Every people of every culture do this.

One of their wise old souls declares, that the earth rides through the heavens on the back of a giant turtle. Isn’t that silly, from your modern educated perch. But the story is not an analogy, it’s not a simplified literal description of the universe like we suppose is given in a science class. It is a Metaphor that allows someone to imagine the world gently moving through the universe freely and with some regularity, returning home to the beach as the seasons change.

The Turtles are referred to at the beginning of Stephen Hawkins famous book ‘A brief history of time’. As this version of the story goes – Bertrand Russell is giving a public lecture on cosmology. He described how the earth orbits around the sun, which orbits around the center of a vast galaxy. At the end of the lecture, a little old lady complains that the lecture is a load of rubbish. She declares that the world is really a plate supported on the back of a giant turtle. After some banter he replies with a smug grin by asking her, what is the turtle standing on? She says, “you’re very clever, young man, but it’s turtles all the way down!”

What we now know is that the Earth is dragged around the sun at 100000 kph which itself is dragged around by the Milky Way at 800000 kph. And it feels like you’re sat still, reading this! I’ve seen a rather dubious suggestion that the old lady was in fact the famous Anthropologist Margaret Mead and her and Bertrand were playing out the story, rather than creating it. I’d like to think so. Either way, there’s a lesson in here for any contemporary scientific views at the raggedy limits of the cutting edge. Let’s say quantum physics – the physicists don’t know exactly how it works yet either and use plenty of figurative turtles to fill in the gaps. I find it kind of comforting that Metaphors are just a form of equation that predates Mathematics. The turtles remain a scientific quandary called the infinite regression and at this point it’s worth noting Fritjof Capra and The Tao of Physics – I’m saying nothing.

Mathematics is the ultimate Metaphor. Replacing real things with an abstract set of symbols that can be constructed in a way as to mimic the behaviours of the things in the real world. Most people would have absolutely no idea what is being represented in the mathematics just by reading the numbers, including other mathematicians.

So, when it comes to thinking about and working with things, that aren’t yet here, or are not directly observable, situated in their entirety, Metaphors and Models are the best form of Representation: R80% in my ongoing nomenclature. There is a problem however with that smaller bloody M word. As people without much insight use it, to refer to anything diagrammatic, but there is an excusable reason for this.

To the uninitiated it is easy to confuse a Diagram with a Model and it’s more than simple semantics. A Diagram that describes a set of discrete parts that make up a thing, a simplification (the reduction of something to fewer components); can easily be confused with a Metaphor that describes the possible effect of the thing, which is a distillation (the extraction of the essential meaning or most important aspects of its affect).

Stop! Look out the window for a moment. Loosen your ombusher and shake your head, this is important. The thing commonly called Mathematical Modelling is NOT one thing, yet most of the proponents wax on about little more than mapping variation in relatively static, repeatable processes under controlled conditions. They are typically based on specifications that exclude all the normal characteristics of anything with signs of life, in favour of all kinds of crappy assumptions more suited to making the sums easier, than to explaining the thing. In other words, the conditions for the mathematics to work are controlled, or simplified to such an extent that they no longer represent anything that actually exists out in the real world. They are just flashy diagrams. Breathe, relax!

George Box, a statistician, has been horribly misquoted for years. He said words to the effect of “all models are wrong, some are useful”. This phrase has been used to excuse the creation of shitty Models. In short, you cannot mathematically model the universe as it is, you can only model your assumptions about some part of it. For the longer version, I suggest reading Murray Gell-Mann. If your Model is wrong, then it is a poor demonstration of your assumptions. But some Models are right and are good predictors of how things actually behave. Their assumptions, the distillation of the most significant characteristics, are close enough to give a reasonable range of possible outcomes for any given set of constraints. A forecast that something is 60% likely to happen is still a good forecast if the thing doesn’t happen, because that was also 40% likely. What George meant was adding additional specificity to your Model will not make it more accurate. The Metaphor is finding the signal in the noise.

Modelling is not about increasing assumptions to a more granular specification, it is about removing the noise and reducing assumptions to a rich distillation. Your collection of assumptions is the Metaphor, that is the Modelling, the mathematics is not the Model. The mathematics is how you can bring it to life to: “watch what it does, test it, take it apart, break it or try to make another one”. That distinct split is not entirely true, as the assumptions are also expressed mathematically, as opposed to being expressed figuratively (Turtles). The adjacent ATOMIC Diagram gives a sense of this mathematical split personality. It’s only a feedback loop and mathematical modelling in its broadest terms, enables you to make millions of cycles in no time at all. Ooh cycles, dynamics, non-linearity, distillations … I shall have to write about Match Speed, Don’t Collide, Head to Centre!

There is however, further out near the edge of that science, some lovely Mathematical Modelling that allows you to play with assumptions and ask all sorts of imaginative questions, to visualise how some system may react under different constraints. In this sense the little architectural cardboard landscape of the city I described in previous posts, as a three dimensional simplification, has a higher purpose.

What you do with that pile of cardboard is to kneel down, squint your eyes at it and try to imagine all those little cardboard people moving around in the landscape, in the sunshine, doing their thing. The cardboard is not a Metaphor, but you use it to stimulate or enact a Metaphor for the world that is already inside your head. If you’d never seen a city before, the cardboard cut-outs would not mean much and you couldn’t visualise how it may function in the real world. Your brain naturally tunes in and responds to the slightest hint of a Metaphor, as long as it’s meaningful to you. Your brain is a big juicy bag of Metaphor that you constantly apply to the world around you, to make sense of it, to become meaningful. Typically, a Model inside your mind is called a Schema and it’s analogy is, mental scaffolding.

So, right at the end of all this cleverness, it would be remiss of me, not to try to distill all these concepts down to something, equally meaningful.

Every child can use Metaphors as they construct, on the fly, ways to imagine the world within and beyond their experience. They use Metaphors freely to solve problems, tell stories and activate themselves, immersed and even momentarily lost, in the magic. We slowly lose this insight as we become older, more sensible and quietly constrained under the illusions of control, deluged upon us by our societal mores. Oh! That came out a bit dark but don’t lose faith.

There are an increasing number artists and artisans and mathematicians who make a good living inspired by that innate sense of the world, looking upwards and outwards with new ways to nurture that curious gaze. So now, like the turtles, you can ‘Go Fourth’ inspired to faithfully represent how your corner of the world could be:

Metaphors are our greatest tool for play, and play our greatest tool for learning.